Formative Assessment Lessons

  • Malcolm Swan
  • Colin FosterEmail author
Part of the ICME-13 Monographs book series (ICME13Mo)


Formative assessment is the process by which teachers and students gather evidence of learning and then use this to adapt the way that they teach and learn in the classroom. In this paper, we describe a design-research project in which we integrated formative assessment into mathematics classroom materials. We outline two examples of formative assessment lessons, one concept-based and the other problem-solving, highlighting the important roles within them of pre-assessment, formative feedback questions, and sample work for students to critique.


Conceptual understanding Formative assessment Problem solving Mathematics task design Teacher professional development 



We would like to thank our Shell Centre designer-researcher colleagues at the University of Nottingham, Nichola Clarke, Rita Crust, Clare Dawson, Sheila Evans and Marie Joubert, along with David Martin and Daniel Pead; the observer-researchers around the US, led by David Foster, Mary Bouck and Diane Schaefer; Alan Schoenfeld, Hugh Burkhardt and Phil Daro, who led the project; and the Bill and Melinda Gates Foundation for the funding that made possible this core contribution to their ‘College and Career Readiness’ strategy for Mathematics.

The ‘Having Kittens’ task was originally designed by Acumina Ltd. ( for Bowland Maths (, and appears courtesy of the Bowland Charitable Trust.


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Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  1. 1.School of EducationCentre for Research in Mathematics Education, University of NottinghamNottinghamUK
  2. 2.School of EducationUniversity of LeicesterLeicesterUK

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